The optimal policy for the one-against-many heterogeneous Lanchester model

We find the optimal fire distribution for the one-against-many Lanchester aimed-fired model, in which a homogeneous Blue force fights a mixed Red force with several distinct types. Each unit of Blue force kills Red type ii at rate bibi, while each type-ii Red unit kills Blue at rate riri. We show that Blue’s optimal dynamical policy is to, at any give time, allocate all its fire to the surviving Red type for which the value of biribiri is highest.